In the figure, O Is the centre of the circle and VA is parallel to XY. ZB = ZA, ∠OXV = 56° and ∠BAZ = 57°. Find
- ∠YXC
- ∠XYZ
(a)
OV = OX = Radius
∠VXO = ∠XVO = 56° (Isosceles triangle, OVB)
∠XOC
= 56° + 56°
= 112° (Exterior angle of a triangle)
OX = OC = Radius
∠OCX
= (180° - 112°) ÷ 2
= 68° ÷ 2
= 34°
∠YXC = 34° (Alternate angles, XY//VE)
(b)
ZB = ZA
∠ZAB = ∠ZBA = 57° (Isosceles triangle ZAF)
∠AZB
= 180° - 57° - 57°
= 66°
∠CZY = ∠AZB = 66° (Vertically opposite angles)
∠XYZ
= 180° - 66°
= 114° (Interior angles)
Answer(s): (a) 34°; (b) 114°